Investigation of 9th Grade Students’ Geometrical Figure Apprehension

Abstract

In the present study, the aim was to investigate 9th grade students’ geometrical figure apprehension. To this end, the Figure Apprehension Cognitive Processes Test (FACPT), constructed by the researchers of the study, was administered to 51 ninth grade students, with whom clinical interviews were also conducted. As a result of the data analysed, it was found that the perceptual, discursive and operative types of apprehension of more than half of the students were not at enough level for high school geometry. Most of the students were found to be unsuccessful in recognizing the various sub-figures present within a geometric figure, in transforming verbal information to visual information, in deriving at verbal information based on visual information, in arriving at conclusions without being influenced by the appearance of a figure, and in decomposing and recomposing geometric figures. This shows that teachers need to focus on not only conceptual knowledge but also the structure of the figure apprehension processes of students prior to geometry classes.

Keywords

• Geometric reasoning,duval’s cognitive model,geometric figure apprehension

References

1. Clements, D. H. (2003). Teaching and learning geometry. Retrieved February 11, 2017 from https://www.researchgate.net/profile/Douglas_Clements/publication/258933229_ Teaching_and_learning_geometry/links/557dd19508aeea18b777c211.pdf
2. Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. The Journal of Mathematical Behavior, 15(4), 375-402.
3. Duval, R. (1995), Geometrical Pictures: kinds of representation and specific processings. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 142-157). Berlin: Springer.
4. Duval, R. (1998). Geometry from a cognitive point of view, In C. Mammana & V. Villani (Ed.), Perspectives on the Teaching of geometry for the 21st century (pp. 37-52). Dordrecht: Kluwer Academic Publishers.
5. Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2), 139-162.
6. Healy, L. & Hoyles, C. (1998). Justifying and proving in school mathematics. Retrieved July 13, 2016 from http://doc.ukdataservice.ac.uk/doc/4004/mrdoc/pdf/a4004uab.pdf
7. Jones, K. (1998). Theoretical frameworks for the learning of geometrical reasoning. Proceedings of the British Society for Research into Learning Mathematics, 18(1-2), 29-34.
8. Llinares, S. & Clemente, F. (2014). Characteristics of pre-service primary school teachers’ configural reasoning. Mathematical Thinking and Learning, 16(3), 234-250.

9. McCrone, S. M. & Martin, T. S. (2004). Assessing high school students’ understanding of geometric proof. Canadian Journal of Math, Science & Technology Education, 4(2), 223-242.
10. Michael – Chrysanthou, P. & Gagatsis, A. (2013). Geometrical figures in geometrical task solving: an obstacle or a heuristic tool? Acta Didactica Universitatis Comenianae – Mathematics, 13, 17-30.
11. Michael, P. (2013). Geometrical figure apprehension: cognitive processes and structure (Unpublished doctoral thesis). The University of Cyprus, Cyprus.
12. Michael, P., Gagatsis, A., Avgerinos, E. & Kuzniak, A. (2011). Middle and High school students’ operative apprehension of geometrical figures. Acta Didactica Universitatis Comenianae–Mathematics, 11, 45, 55.
13. Ministry of National Education [MoNE] (2013a, 2018a). High school mathematics curriculum (9, 10, 11 and 12. grades). Ankara: MoNE Publication, Turkey
14. Ministry of National Education [MoNE] (2013b, 2018b). Secondary school mathematics curriculum (5, 6, 7, and 8. grades). Ankara: MoNE Publication, Turkey
15. Parzysz, B. (1991). Representation of space and students' conceptions at high school level. Educational Studies in Mathematics, 22(6), 575-593.
16. Senk, S. L. (1985). How well do students write geometry proofs? Mathematics Teacher, 78, 448-456.
17. Torregrosa, G. & Quesada, H. (2008). The coordination of cognitive processes in solving geometric problems requiring proof. In O. Figueras & A. Sepulveda (Eds.), Proceedings of the Joint Meeting of PME (Vol. 32, pp. 321-328). Mexico: PME.
18. Ubuz, B. (1999). 10. ve 11. sinif ogrencilerinin temel geometri konularindaki hatalari ve kavram yanilgilari [10th and 11th grade students’ basic geometry errors and misconceptions on the subject]. Hacettepe Universitesi Egitim Fakultesi Dergisi, 16-17, 95-104.